Advertisements
Advertisements
प्रश्न
Two bodies of masses m and 4m are placed at a distance of r. Calculate the gravitational potential at a point on the line joining them where the gravitational field is zero.
Advertisements
उत्तर
Let the point be the position when the gravitational field is zero.,
`("Gm")/"x"^2 = ("G"(4"m"))/("r" - "x")^2`
`1/"x"^2 = 4/("r" - "x")^2`
Square root on both sides,
`1/"x" = 2/(("r" - "x"))`
∴ x = `"r"/3`
The point P is at a distance `"r"/3` from mass ‘m’ and `"2r"/3` from mass ‘4m’
Gravitational potential V = `(-"Gm")/(("r"/3)) - ("G"(4"m"))/(("2r"/3))`
= `(-3"Gm")/4 - (3"G"(4"m"))/(2"r")`
= `(-3"Gm")/"r" - (12"Gm")/(2"r")`
V = `(-9"Gm")/"r"`
APPEARS IN
संबंधित प्रश्न
If the masses of the Earth and Sun suddenly double, the gravitational force between them will ___________.
A planet moving along an elliptical orbit is closest to the Sun at distance r1 and farthest away at a distance of r2. If v1 and v2 are linear speeds at these points respectively. Then the ratio `"v"_1/"v"_2` is
If the distance between the Earth and Sun were to be doubled from its present value, the number of days in a year would be ___________.
Define gravitational potential energy.
Is potential energy the property of a single object? Justify.
Define gravitational potential.
What is the difference between gravitational potential and gravitational potential energy?
The work done by Sun on Earth in one year will be
Earth revolves around the Sun at 30 km s−1. Calculate the kinetic energy of the Earth. In the previous example, you calculated the potential energy of the Earth. What is the total energy of the Earth in that case? Is the total energy positive? Give reasons.
An object is thrown from Earth in such a way that it reaches a point at infinity with non-zero kinetic energy `["K"."E"("r" = ∞) = 1/2 "Mv"_"∞"^2]`, with what velocity should the object be thrown from Earth?
